Question

two wires A and B are of equal length and have equal rasistance . if resistivity of A is more than B which wire is thicker and wh

Answer 1

HEY mate here is your answer.

as given both wires have equal resistances, area of crossection of A must be thicker.

because it is inversely proportional.

hope it helps you

Answer 2

Given,

Length of wire A = length of wire B

Resistance of wire A = Resistance of wire B

The resistivity of wire A > resistivity of wire B

To find,

The thicker wire among A and B.

Solution,

We can simply solve this numerical problem by using the following process:

Mathematically,

Resistance of a wire

= (resistivity of the wire)(length of the wire) / (area of the cross-section of the wire)

{Equation-1}

Let us assume that;

resistance of wire A = RA

the resistivity of wire A = rhoA

length of wire A = LA

area of cross-section of wire A = AA

resistance of wire B = RB

the resistivity of wire B = rhoB

length of wire B = LB

area of cross-section of wire B = AB

Now, according to the question;

Resistance of wire A = Resistance of wire B

=> RA = RB

=> (resistivity of the wire A)(length of the wire A)/(area of the cross-section of the wire A) = (resistivity of the wire B)(length of the wire B)/(area of the cross-section of the wire B)

{Using equation-1}

=> (rhoA)(LA)/(AA) = (rhoB)(LB)/(AB)

=> (rhoA)/(AA) = (rhoB)/(AB) {Equation-2}

(Since the length of both wires is equal)

Now, according to the question, in equation-2;

(rhoA)/(AA) = (rhoB)/(AB), where,

rhoA > rho B

=> AA > AB (mathematically)

=> area of cross-section of wire A > area of cross-section of wire B

=> wire A is thicker than wire B

Hence, the area of cross-section of wire A is greater than the area of cross-section of wire B, that is, wire A is thicker than wire B.